Help easy question. MATH

Question

Starting with the expression for the standard parabola y = x^2

deduce the sequence of transformations needed to create the graph of the function y = -3(x + 2)^2 – 7

Note: For instance, if we were given the function y = -3|x – 4| + 1

we would start with the absolute value function y = |x| and the sequence of transformations would be:

- Shift right 4 units, yielding y = |x – 4|

- Stretch by a factor of 3, yielding y = 3|x – 4|

- Reflect about the x-axis, yielding y = -3|x – 4|

- Shift upward 1 unit, yielding y = -3|x – 4| + 1

b. Graph each transformation in the sequence on the same set of axes.

Answer 1

Use the same pattern as your example:

Start with the squaring function y = x² and perform this sequence of transformations:

- Shift left 2 units, yielding y = (x + 2)²

- Stretch by a factor of 3, yielding y = 3(x + 2)²

- Reflect about the x-axis, yielding y = -3(x + 2)²

- Shift downward 7 units, yielding y = -3(x + 2)² - 7